Phase transition of hadronic matter in a non-equilibrium approach

Graduate Days, Frankfurt, 18.06.08, Hannah Petersen, Universität Frankfurt

Hannah Petersen Graduate days, 18.06.08 2

Thanks to…

My collaborators: Gerhard Burau Jan Steinheimer Marcus Bleicher Horst Stöcker

For providing the hydro code: Dirk Rischke

For financial support:

Hannah Petersen Graduate days, 18.06.08 3

Outline

Motivation Model Description and Parameter

Tests Time Evolution and Final State

Interactions Multiplicities and Spectra <mT> Excitation Function Conclusion and Outlook

-> all the information can be found in H.P. et al., arxiv:0806.1695

Hannah Petersen Graduate days, 18.06.08 4

Motivation

Fix the initial state and freeze-out learn something about the EoS and the effect of viscous dynamics

1) Non-equilibrium

initial conditions

via UrQMD

2) Hydrodynamic evolution or Transport calculation

3) Freeze-out via

hadronic cascade

(UrQMD)

Hannah Petersen Graduate days, 18.06.08 5

Are differences between hydro and transport as big as expected?

Investigation of differences between UrQMD:

non-equilibrium (Boltzmann) transport approach

hadron-string and resonance dynamics

UrQMD+Hydro: non-equilibrium initial conditions ideal hydrodynamic evolution for the

hot and dense phase Freeze-out via hadronic cascade

Hannah Petersen Graduate days, 18.06.08 6

Initial State I coupling between UrQMD initial state and

hydrodynamic evolution at:

contracted nuclei have passed through each other

initial NN scatterings have proceeded energy is deposited

hadrons are represented by a Gaussian with finite width

with the proper normalisation(J.Steinheimer et al., Phys.Rev.C77:034901,2008, arXiv:0710.0332)

Hannah Petersen Graduate days, 18.06.08 7

Single Event – Initial State

Energy density distribution at Elab=40 AGeV,

thydrostart = 2.83 fm, tsnapshot = 3.07 fm

Event-by-event fluctuations are naturally taken into account

Hannah Petersen Graduate days, 18.06.08 8

(3+1)d Hydrodynamic Evolution

Ideal relativistic one fluid hydrodynamics

and

Hadron gas equation of state (EoS) No phase transition included Baseline check All hadrons with masses up to 2.2 GeV are

included (consistent with UrQMD) (D. Rischke et al., Nucl. Phys. A 595, 346 (1995))

Hannah Petersen Graduate days, 18.06.08 9

Freeze-out

hydrodynamic evolution until < 730 MeV/fm³ (≈ 5 * 0) in all cells

isochronous freeze-out is performed via the Cooper-Frye formula

with boosted Fermi or Bose distributions f(x,p) including B and S

rescatterings and final decays calculated via hadronic cascade (UrQMD)

Hannah Petersen Graduate days, 18.06.08 10

Freeze-out IIDistribution of the cells at freeze-out

->Important inhomogeneities are naturally taken into account (A.Dumitru et al., Phys. Rev. C 73, 024902 (2006))

Hannah Petersen Graduate days, 18.06.08 11

Freeze-out line

Parametrization of chemical freeze-out line taken from Cleymans et al,

J.Phys. G 32, S165, 2006

Mean values and widths are in line with other calculations

Hannah Petersen Graduate days, 18.06.08 12

Dependence on Freeze-out

Variation of the freeze-out criterium does not affect the meson multiplicities

Higher values are for Elab=40 AGeV while lower values are for Elab=11 AGeV

Hannah Petersen Graduate days, 18.06.08 13

Dependence on tstart

Variation of starting time by a factor 4 changes results only by 20 %

Hannah Petersen Graduate days, 18.06.08 14

Time scales

Hannah Petersen Graduate days, 18.06.08 15

Final State Interactions

Hannah Petersen Graduate days, 18.06.08 16

Baryon density distribution

Time evolution of the baryon density is smooth

1) in the reaction plane

2) in a central cell

Hannah Petersen Graduate days, 18.06.08 17

Time Evolution

-> UrQMD equilibrates to a rather large degree

Hannah Petersen Graduate days, 18.06.08 18

Multiplicities

Both models are purely hadronic without phase transition, but different underlying dynamics

results for particle multiplicities from AGS to SPS are surprisingly similar

strangeness is enhanced in the hybrid approach due to local equilibration

full lines: hybrid modeldotted lines: UrQMD-2.3

symbols: experimental data

K P

Hannah Petersen Graduate days, 18.06.08 19

Rapidity Spectra

-> Rapidity spectra for pions and kaons have a very similar shape in both calculations

Hannah Petersen Graduate days, 18.06.08 20

mT spectra Blue: pionsGreen: protonsRed: kaons

mT spectra are very similar at lower energies (11,40 AGeV)

<mT> is higher in hydro calculation at Elab=160 AGeV

Hannah Petersen Graduate days, 18.06.08 21

<mT>Excitation Function

Resonance excitations and non-equilibrium effects in intermediate energy regime lead to a softening of the EoS in pure UrQMD calculation

hybrid calculation with hadronic EoS just rises as a function of beam energy

Hannah Petersen Graduate days, 18.06.08 22

Conclusion and Outlook

First results from the comparison of a transport and a hybrid calculation with the same initial conditions and freeze-out Multiplicities are surprisingly similar Strangeness is enhanced due to local equilibration <mT> excitation function is different

Further studies of different EoS with explicit phase transition are needed

Calculations at higher energies (RHIC)